It will be better than today’s Times Square II; how Times Square III compares with Times Square I will be for future generations to say. But I’m willing to be optimistic, because we’ll need all the optimism we can summon after whichever 1980s-nostalgic Democrat succeeds Mayor Bloomberg.

New Times Square I was the safe, family- and commercial-friendly one (“Disneyfied” to idiots) which replaced the squalid mugging and pimping ground of the 1970s-mid 1990s.

New Times Square II was foisted on us by the Department of Transportation in 2009 — when Broadway was closed to traffic from 42nd-47th streets to create the ugliest “plazas” outside a prison yard, so filled with immobile, low-rent tourists that David Letterman called it a “petting zoo.”

Ever since, locals who falsely claimed never to go to Times Square truly do not; in its zeal to coddle visitors, City Hall managed to entirely alienate New Yorkers from an iconic district they once merely begrudged. Even superannuated hippies, who would transform all of Manhattan into a car-free bike zone given the chance, admitted the pedestrian lolling grounds — of blue asphalt and full of trailer-park chairs and planters — were ghastly.

New Times Square III, to begin installation this fall and be completed in 2015, aims to replenish the lost energy of the “bowtie.” Having spent a mere $1 million on the 2009 mess, the city will now spend $40 million to try fixing it.

The job, by architectural firm Snohetta Design, will banish the current, two-level confusion and clutter of Broadway sidewalks and “plazas” for a single surface of dark, two-tone concrete on each of the five open pedestrian spaces.

Steel discs embedded in the new pavement are supposed to twinkle to the whims of the bowtie’s 24-7, night-into-day LED blaze. Massive, built-in benches of black granite will partially separate former sidewalks from the mid-Broadway grazing round. The idea is to concentrate gawkers in the center, to facilitate purposeful, normal walking where sidewalks now are, and restore the Broadway Boogie-Woogie energy dissipated by immobile, sandwich-chomping tourists.

Times Square III looks good on paper. But renderings and models often lie: Remember when the battleship-gray New York Times tower was promoted as a “shimmering white mirage?”

It’s possible the Snohetta plan will yield merely Times Square II.5 — improving upon the current eyesore but falling short of a miraculous metamorphosis.

The architects promised The Post last year the new look would be “muscular” with a “film noir” feel, and “not taking its cues from some pretty little things in Europe.”

At least today’s unintelligible jumble of blue and gray surfaces, turning lanes, barricades, planters, pylons and out-of-place signs — equally baffling to motorists and walkers — will give way to a more visually coherent stage. It might even make big-bellied day-trippers walk a little faster.

Of course, if you hate the plazas as much as any normal cranky New Yorker, you’re right to be skeptical. Even if the new ones are Pritzker Prize material, they can’t bring back Times Square’s old nighttime dynamism, conveyed in oft-photographed streams of headlights converging and diverging. Autos do help fire the urban energy grid, even if Copenhagen-addled academics don’t get it.

I’ve written for years about the inappropriateness of DOT Commissioner Janette Sadik-Khan’s wholesale remaking of Times Square without meaningful public oversight or environmental review.

I deplored the destructive impact on the “built environment” of a Times Square that’s pedestrian-clogged without really being pedestrian-friendly; it takes as long to walk the bowtie’s length as it ever did, and even some tourists look annoyed.

Maybe the new plan is just a tactic to ensure that a future mayor can’t easily throw the plazas out and restore the old traffic pattern.

But — gulp — the plazas aren’t going anywhere. They’re just too popular at a time hotels are going up on every block and the city needs every tourist dime it can get.

They’re packed even on windblown winter nights, while Sadik-Khan’s citywide bicycle lanes remain little used in perfect weather. Thanks to a (for now) crime-free environment, it’s fun to wallow amidst Times Square’s physical pleasures — the embrace of old and new buildings that feel humane despite their often great sizes, and an LED bath less romantic but brighter than neon ever was.

And the market has spoken. Real-estate brokers once worried that companies would leave Times Square’s office towers, their highly paid employees disgusted by hordes of slovenly dressed bus-tour visitors. But Viacom not only just renewed its million-square-foot lease at 1515 Broadway through 2031, it expanded by 300,000 more square feet — one of the largest commitments in Manhattan history.

So maybe, in tapping the Snohetta design, Bloomberg wasn’t merely trying to protect Times Square II from a future mayor who might have other ideas.

Maybe he listened to those of us who called the current plaza design for what it is — “dopey colored circles that seem the work of preschoolers . . . an affront to Times Square’s historic central role in the life of the city and to the power and glory of its landmarks,” I called it at the time.

Can $40 million buy back what was lost? We won’t know for sure until after Bloomberg has left City Hall — too late to undo what he made of Times Square, but not too early to cheer or cry over it.